| Description |
This paper proposes to study conditions under which the solutions of second-order linear differential equations will oscillate, that is, conditions under which solutions will pass through the equilibrium position zero infinitely many times. In the literature under consideration, to say that "the solutions of an equation oscillate" is equivalent to saying "the equation is oscillatory"; both terms will be used in this paper. We begin with Sturm's classical comparison theorem and trace the historical development of theorems for oscillation of solutions through several authors, namely Fite, Wintner, Leighton, Hartman, Coles, Willett, Hinton and Lewis, and end with extensions to the matrix case by Byers, Harris, and Kwong. |
